The Midlands side dominated possession in their first appearance on the main stage of a European competition since 1980, but a sloppy pass from Ryan Bennett allowed Braga to steal a vital advantage with the only goal of the game.
Ricardo Horta, scorer of three goals in qualifying, lashed home a powerful shot off an upright to send the tiny pocket of travelling fans into delirium.
The defeat was a third in succession for Nuno Espirito Santo’s team after Premier League losses against Everton and Chelsea.
Molineux was rocking for Wolves return to European football after 39 years but the first half was a subdued affair; the home side bossing possession without managing to create too many decent scoring chances. The high-tempo game that served Wolves so well last season didn’t get going.
Leander Dendoncker had the best chance of the night for the hosts not long after half-time, but his effort from close range was saved Matheus in the Braga goal.
Braga rarely threatened, with their only shot on target in the first 70 minutes a tame Paulinho effort. Wolves meanwhile were growing in stature the longer the contest wore on.
The game was being played more and more in the Braga half but, on 71 minutes, disaster for the Premier League side.
Bennett’s casual pass from just inside his own half was seized upon by Wanderson Galeno. The forward was able to drive at the retreating defence and, with option to choose from inside the box, he picked out the perfect low pass into the path of Horta.
The winger had time to control and steady himself before driving a powerful shot in off Rui Patricio’s upright.
Braga, Europa League finalists in 2011, were camped in their own half as the clock wound down but Wolves couldn’t find the leveller, Raul Jimenez flicking a header wide of goal in the final minute of stoppage time.
In the other Group K clash, Slovan Bratislava came from behind on their own patch to overcome Besiktas 4-2.